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  <h1> Calculation questions</h1>
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These questions were examined in the past exam questions.
<p>Note: when making assumptions, you need to clearly state the reasons.</p>
<p>For example, the expected inflation is likely to be around the inflation target of the government. </p>
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    Income cover
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      EBIT (earnings before interest and tax) / (annual interest + annual interest for all prior assets)
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    Capital cover (asset cover)
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      current liabilities are paid off, goodwill was removed from assets (make this statement before doing any calculations)
      <br>
      Remaining capital / (capital value of the asset and any prior assets) = (Debtors+Stock+Cash)-(Creditors+Overdraft+Tax Reserve)
      <br>
      Remember to produce adjusted balance sheet!
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    Expected vs required return
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      Expected return = running yield + expected growth rate
      <br>
      Expected return = running yield + expected inflation + expected real growth rate
      <br>
      Required return = risk-free rate of return + expected inflation + risk premium
      <ul>
        <li>
          For index-linked bonds, the required return always equals the expected return
        </li>
        <li>
          For conventional bonds, the expected return is exactly the yield in the market
        </li>
      </ul>
      Compare relative attractiveness of index-linked bonds and asset x
      <ul>
        <li>As the expected return equals the required return for index-linked bonds, only
        the expected return and the required return for the asset x need to be compared.
        </li>
      </ul>
      Compare the relative attractiveness of equities and conventional bonds
      <ul>
        <li> Traditional method: yield gap: gross dividend yield on equities - GRY on benchmark long-dated bond
        </li>
        <li> Traditional method: reverse yield gap: GRY on benchmark long-dated bond - gross dividend yield on equities
        </li>
        <li> Practical method: GRY − d = inflation risk premium − equity risk premium + g
          <ul>
            <li> GRY is the gross redemption yield of bond
            </li>
            <li> d represents the gross dividend yield on equities
            </li>
            <li> g is the nominal growth rate of the equities, it equals expected inflation + real growth rate
            </li>
            <li> If left hand side of the equation is larger, the conventional bonds appear to give better value
            </li>
            <li> On the contrary, if right hand side is larger, the equities give better value
            </li>
          </ul>
        </li>
      </ul>
      Compare the relative attractiveness of properties and equities
      <ul>
        <li>  yield gap can be defined as: PRP − expected rental growth − (ERP − expected dividend growth)
        </li>
      </ul>
      Compare the relative attractiveness of properties and conventional bonds
      <ul>
        <li> rental yield − GRY = PRP − expected rental growth − IRP
        </li>
      </ul>
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      value of the share to the investor:  $\frac{D_1}{r-g} $
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      the investor’s required dividend yield: $\frac{d}{p}=r-g$
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      target price earnings ratio: $ \frac{p}{e} = (d/e)/(r‐g)$
    . Note d/e is the pay-out ratio
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      When comparing the required return and the expected return. We make the following simplifying assumptions:
      <ul>
        <li>all investors want a real return (rather than a nominal return)
        </li>
        <li>all investors have the same investment time horizon
        </li>
        <li>tax differences between investors can be ignored
        </li>
        <li>reinvestment occurs at a rate equal to the expected return on the given asset
        </li>
      </ul>
      main components of the corporate bond risk premium
      <ul>
        <li>inflation risk premium, premium to compensate for higher risk of default, premium to compensate for lower marketability.
        </li>
      </ul>

      main components of the equity risk premium
      <ul>
        <li>premium to compensate for higher risk of default,
        </li>
        <li>premium to compensate for lower marketability,
        </li>
        <li>premium to compensate for greater volatility (or uncertainty) in both income and capital.
        </li>
      </ul>
      How will the property risk premium differ from the equity risk premium above?
      likely to be higher to compensate for
      <ul>
        <li> poor marketability,
        </li>
        <li> high dealing and management costs,
        </li>
        <li> risk of voids,
        </li>
        <li> risk of depreciation and obsolescence. this might be offset slightly by lower income and capital volatility in short term.
        </li>
      </ul>

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    the DCF value of the notional portfolio
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      the DCF value of the notional fixed-interest bond portfolio is given by:
      <br>
      $\frac{p \times M_{all}}{M_{b}}\times DC_b$
      <br>
      where
      <ul>
        <li>p represents the proportion of portfolio in bond
        </li>
        <li>$M_{all}$ representsthe total market value
        </li>
        <li>  $M_b$ represents the market value of the bond
        </li>
        <li>$DC_b$ represents discount cash flow value of the bond
        </li>
      </ul>
    Hence, the total value of the notional portfolio is given by the aggregation of the notional value of all assets
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  <p> Author: Mengke, Lyu</p>

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